An electrical signal flows through conductive materials as a current. In certain cases, the current may flow from one conductive material into another at a junction, or contact, between the materials. Resistance to the flow of current is inversely proportional to area. Thus, in order to minimize resistance and maximize the current flow from one material into the other, the contact area, or overlap, between the two materials is as large as possible.
All materials change their size when subjected to a change in temperature. A property known as the coefficient of thermal expansion describes how the size of an object changes in response to a change in temperature. Specifically, it measures the fractional change in size per degree change in temperature. Different materials have different coefficients of thermal expansion and thus, react differently (i.e., the sizes change by different amounts) when subjected to a temperature change. Generally, the change in area can be expressed as ΔA/A=αA·ΔT, where A is the area, αA·is the thermal expansion coefficient, and T is the temperature.
In certain cases, two layers of different materials having different coefficients of thermal expansion may be overlapped in an area in order to allow current to flow between the materials. As the temperature changes, the two materials may expand or contract at a different rates. At a certain point, a shear force formed by the changes in size may cause bonds between the materials to break, resulting in one material peeling away from the other. The larger the area of overlap between the materials, the stronger that force becomes, resulting in the materials peeling apart more easily. Thus, in order to prevent the materials from coming apart the area of overlap is small. This is in conflict with the large size used to lower resistance. Thus, circuit designers face a dilemma when trying to balance a large contact area to reduce resistance and a small contact area to prevent separation due to thermal expansion.